13 citations · 24 across the 8 of their papers we have counts for
9 papers
Large-time behavior of solutions of parabolic equations on the real line with convergent initial data III:unstable limit at infinity
Antoine Pauthier, Peter Poláčik
This is a continuation, and conclusion, of our study of bounded solutions of the semilinear parabolic equation on the real line whose initial data $u_0=u(\cdo…
Weak and strong interaction of excitation kinks in scalar parabolic equations
Antoine Pauthier, Jens D. M. Rademacher, Dennis Ulbrich
Motivated by studies of the Greenberg-Hastings cellular automata (GHCA) as a caricature of excitable systems, in this paper we study kink-antikink dynamics in the perhaps simplest…
Large-time behavior of solutions of parabolic equations on the real line with convergent initial data II: equal limits at infinity
Antoine Pauthier, Peter Poláčik
We continue our study of bounded solutions of the semilinear parabolic equation on the real line, where is a locally Lipschitz function on Assum…
Advection-diffusion dynamics with nonlinear boundary flux as a model for crystal growth
Antoine Pauthier, Arnd Scheel
We analyze the effect of nonlinear boundary conditions on an advection-diffusion equation on the half-line. Our model is inspired by models for crystal growth where diffusion model…
Large-time behavior of solutions of parabolic equations on the real line with convergent initial data
Antoine Pauthier, Peter Poláčik
We consider the semilinear parabolic equation on the real line, where is a locally Lipschitz function on We prove that if a solution of this…
Entire solution in cylinder-like domains for a bistable reaction-diffusion equation
Antoine Pauthier
We construct nontrivial entire solutions for a bistable reaction-diffusion equation in a class of domains that are unbounded in one direction. The motivation comes from recent resu…
Road-field reaction-diffusion system: a new threshold for long range exchanges
Antoine Pauthier
We consider reaction-diffusion equations of KPP type in a presence of a line of fast diffusion with non-local exchange terms between the line and the framework. Our study deals wit…
Uniform dynamics for Fisher-KPP propagation driven by a line of fast diffusion under a singular limit
Antoine Pauthier
The purpose of this paper is to understand the links between a model introduced in 2012 by H. Berestycki, J.-M. Roquejofre and L. Rossi and a nonlocal model studied by the author i…
The influence of a line with fast diffusion and nonlocal exchange terms on Fisher-KPP propagation
Antoine Pauthier
A new model to describe biological invasion influenced by a line with fast diffusion has been introduced by H. Berestycki, J.-M. Roquejoffre and L. Rossi in 2012.The purpose of thi…